In this example, we introduce the use of a sparse derived set with a membership filter. Using a membership filter is the third method for defining a derived set. When you define a set using this method, you specify a logical condition each member of the set must satisfy. LINGO then filters out potential set members that don't satisfy the membership condition.

For our example, we will formulate a matching problem. In a matching problem, there are N objects we want to match into pairs at minimum cost. The pair (I,J) is indistinguishable from the pair (J,I). Therefore, we arbitrarily require I be less than J in the pair. Formally, we require I and J make a set of ordered pairs. In other words, we do not wish to generate redundant ordered pairs of I and J, but only those with I less than J. This requirement that I be less than J will form our membership filter.

The file containing this model may be found in the SAMPLES subdirectory off the main LINGO directory under the name MATCHD.